Problem: A circle with area $36\pi$ has a sector with a $90^\circ$ central angle. What is the area of the sector? ${36\pi}$ $\color{#9D38BD}{90^\circ}$ ${9\pi}$
The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{90^\circ}{360^\circ} = \dfrac{A_s}{36\pi}$ $\dfrac{1}{4} = \dfrac{A_s}{36\pi}$ $\dfrac{1}{4} \times 36\pi = A_s$ $9\pi = A_s$